Given that a firm's shares are trading at two times the book value and it is anticipated that the firm will earn a 14% return on book value next year, we need to calculate the expected return on buying this stock for the following forecasts of residual earnings growth after the forward year: 4%, 6%, and 8%.Calculation for expected returnThe expected return can be calculated as follows:Expected return = Dividend yield + Capital gain yieldWhere,Dividend yield = Dividend / Market price of the stockCapital gain yield = (Price of stock after one year - Price of stock today) / Price of stock todayDividend yieldWe don't know the dividend, so we can't calculate the dividend yield. We can suppose a dividend yield of zero.Capital gain yieldLet's use the following variables:P0 = Market price of stock today;D1 = Dividend expected at the end of year 1;R = Return on book value;g = Residual earnings growth;So, the price of stock after one year can be expressed as:P1 = P0 * (1 + R * (1 - g))And the capital gain yield can be written as:Capital gain yield = (P1 - P0) / P0Substituting the given values in the equation, we have:For g = 4%:P1 = P0 * (1 + 14% * (1 - 4%)) = 1.1892 * P0Capital gain yield = (1.1892 * P0 - P0) / P0 = 0.1892For g = 6%:P1 = P0 * (1 + 14% * (1 - 6%)) = 1.2684 * P0Capital gain yield = (1.2684 * P0 - P0) / P0 = 0.2684For g = 8%:P1 = P0 * (1 + 14% * (1 - 8%)) = 1.3504 * P0Capital gain yield = (1.3504 * P0 - P0) / P0 = 0.3504If no growth is expected, then g = 0%:P1 = P0 * (1 + 14% * (1 - 0%)) = 1.14 * P0Capital gain yield = (1.14 * P0 - P0) / P0 = 0.14Hence, the expected return on buying this stock for the following forecasts of residual earnings growth after the forward year: 4%, 6%, and 8% is 18.92%, 26.84%, and 35.04%, respectively, and the expected return if no growth is expected is 14%.